The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  1  X  1  1  X  1  1  X  X  X  1  2  0  X  1  X  X  2  0  X  2  X  1  X  2  2  0  X  1  2  X  1
 0  2  0  2  0  2  0  2  0  2  0  2  0  2  0  2  0  2  2  0  2  2  0  2  2  0  2  0  2  0  0  2  2  0  2  2  0  2  2  2  0  0  0  0  0  2  2  2  2  0  0  0

generates a code of length 52 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 54.

Homogenous weight enumerator: w(x)=1x^0+1x^54+10x^55+1x^56+2x^57+1x^58

The gray image is a code over GF(2) with n=208, k=4 and d=108.
This code was found by Heurico 1.16 in 0.0476 seconds.